The equation solved is f(x, y, z, u) = x + y * y + z * z * z + u * u * u * u = o.
Blog Entry (c) Monday, January 20, 2025, by James Pate Williams, Jr. Solution of a Nonlinear Equation Using a Back-Propagation Neural Network
Category: C Applications
Blog Entry © Saturday, January 18, 2025, by James Pate Williams, Jr. Preliminary Virtual Vision Field (VVF) Diagnostic Optometry Test Simulator
I was administered a VVF Test on Wednesday, January 15, at Dr. Brent Brown and Associates Inc office in LaGrange, Georgia. The test consists of using a headset that has an orange circle in the center of the display. The examinee has a trigger device to click each time a white flash occurs. I decided to write a C/C++ Win32 application to simulate the VVF Test. The following two pictures are from a simulated test of one minute in duration. The white flashes are separated by 1000 millisecond (1 second) and their durations are also 1000 milliseconds (1 second).
Positions of the Hits
1 (571, 842)
2 (587, 196)
3 (594, 644)
4 (694, 273)
5 (717, 620)
6 (718, 297)
7 (724, 360)
8 (743, 186)
9 (774, 736)
10 (798, 326)
11 (835, 361)
12 (859, 357)
13 (927, 553)
14 (1040, 848)
15 (1100, 463)
16 (1177, 157)
17 (1195, 552)
18 (1225, 190)
19 (1234, 344)
20 (1253, 606)
21 (1285, 872)
22 (1290, 594)
23 (1297, 391)
24 (1303, 458)
Positions of the Misses
1 (627, 832)
2 (983, 266)
3 (1078, 827)
4 (1191, 788)
5 (1258, 349)
6 (1317, 585)
Blog Entry © Tuesday, January 7 – Thursday, January 9, 2025, by James Pate Williams, Jr. Solution of a System of Nonlinear Equations Using Damped Newton’s Method for a System of Equations
Live Person-to-Person Tutoring
Blog Entry © Tuesday, October 29, 2024, by James Pate Williams, Jr. Second Order Quantum Mechanical Perturbation Calculation Part II
Blog Entry (c) Monday September 16, 2024, by James Pate Williams, Jr. Ramanujan Highly Composite Numbers
Ramanujan Highly Composite Numbers
## 2 3 5 7 11 13
1 2 1
2 4 2
3 6 1 1
4 12 2 1
5 24 3 1
6 36 2 2
7 48 4 1
8 60 2 1 1
9 120 3 1 1
10 180 2 2 1
11 240 4 1 1
12 360 3 2 1
13 720 4 2 1
14 840 3 1 1 1
15 1260 2 2 1 1
16 1680 4 1 1 1
17 2520 3 2 1 1
18 5040 4 2 1 1
19 7560 3 3 1 1
20 10080 5 2 1 1
21 15120 4 3 1 1
22 20160 6 2 1 1
23 25200 4 2 2 1
24 27720 3 2 1 1 1
25 45360 4 4 1 1
26 50400 5 2 2 1
27 55440 4 2 1 1 1
28 83160 3 3 1 1 1
29 110880 5 2 1 1 1
30 166320 4 3 1 1 1
31 221760 6 2 1 1 1
32 277200 4 2 2 1 1
33 332640 5 3 1 1 1
34 498960 4 4 1 1 1
35 554400 5 2 2 1 1
36 665280 6 3 1 1 1
37 720720 4 2 1 1 1 1
38 1081080 3 3 1 1 1 1
39 1441440 5 2 1 1 1 1
40 2162160 4 3 1 1 1 1
Runtime in seconds = 182.490
Type any character to exit application
Blog Entry (c) Tuesday September 3, 2024, by James Pate Williams, Jr.
Blog Entry (c) Saturday August 31, 2024, by James Pate Williams, Jr. An Elementary School Problem Found Online
Solve for a real root of the equation
f(x)=log6l(5+x)+log6l(x)=0
First we test our log6l(x) function
log6l(12) = 1.386853
log6l(36) = 2.000000
x = 0.1925824036
f = 0.0000000000
Blog Entry (c) Friday August 30, 2024, by James Pate Williams, Jr. Another Simple Math Problem
We use an evolutionary hill-climber and the solution of the quadratic equation to solve the easy problem below:
Solution of f(a,x)=sin(sqrt(ax-x^2))=0
Subject to the constraint x+y=100
Where x and y are the two roots of
g(a,x)=ax-x^2-n*n*pi*pi=0
and n=15
a = 100.347888933988
x = 32.947113268776
y = 67.400775665213
g = 0.000000000000
s = 100.347888933988
runtime in seconds = 43.730000
Numerical Explorations 